# Cone Clutch

Friction clutch with conical plates that engage when normal force exceeds threshold

Clutches

## Description

This block represents a friction clutch with a conical contact interface. The conical interface creates a wedging action between the clutch components, a cone and a cup, thereby reducing the normal force required for clutch engagement.

The cup component connects rigidly to the drive shaft, spinning with it as a unit. The cone component connects rigidly to the driven shaft, which sits in axial alignment with the drive shaft. The clutch engages when the cone slides toward the cup and presses tightly against its internal surface.

Friction at the cone-cup contact interface enables the clutch to transmit rotational power between the drive and driven shafts. The friction model of this block includes both static and kinetic friction contributions, the latter of which leads to power dissipation during slip between the cone and cup components.

Cone clutches find real-world application in synchromesh gearboxes, which synchronize the drive and driven shaft speeds to enable smoother engagement between transmission gears. For block model details, see Cone Clutch Model.

## Cone Clutch Model

The Cone Clutch is based on the Fundamental Friction Clutch. For the complete friction clutch model, consult the Fundamental Friction Clutch block reference page. This section discusses the specialized model implemented in the Cone Clutch.

When you apply a normal force FN, the Cone Clutch block can apply two kinds of friction to the driveline motion, kinetic and static. The clutch applies kinetic friction torque only when one driveline axis is spinning relative to the other driveline axis. The clutch applies static friction torque when the two driveline axes lock and spin together. The block iterates through multistep testing to determine when to lock and unlock the clutch.

### Clutch Geometry and Variable Summary

The figure shows the cone clutch geometry and some model parameters. Refer to the table for a summary of variable descriptions.

Clutch Variables

ParameterDefinitionSignificance
doOuter diameter of the conical contact surfaceSee the preceding figure
diInner diameter of the conical contact surfaceSee the preceding figure
αCone half angleSee the preceding figure
ωRelative angular velocity (slip)ωFωB
ωTolSlip tolerance for clutch lockingSee the following model
FNNormal force applied to conical surfacesNormal force applied, if greater than threshold: FN > Fth
αCone half-angleSee the preceding figure
reffEffective torque radiusEffective moment arm of clutch friction force
kKKinetic friction coefficientDimensionless coefficient of kinetic friction of conical friction surfaces. Function of ω.
kSStatic friction coefficientDimensionless coefficient of static friction of conical friction surfaces.
τKKinetic friction torqueSee the following model
τSStatic friction torque limit(static friction peak factor)·(kinetic friction torque for ω → 0)
(See the following model)

### Relation to Fundamental Friction Clutch

The Cone Clutch is based on the Fundamental Friction Clutch. Instead of requiring the kinetic and static friction limit torques as input signals, the Cone Clutch calculates the kinetic and static friction from the clutch parameters and the input normal force signal FN. See the Fundamental Friction Clutch reference page for more information about the friction clutch.

#### Kinetic Friction

The kinetic friction torque is the product of four factors:

τK = kK·FN·reff·sgn(ω) .

The kinetic friction torque opposes the relative slip and is applied with an overall minus sign. It changes sign when ω changes sign.

You specify the kinetic friction coefficient kK as either a constant or a tabulated discrete function of relative angular velocity ω. The tabulated function is assumed to be symmetric for positive and negative values of the relative angular velocity, so that you need to specify kK for positive values of ω only.

The effective torque radius reff is the effective radius, measured from the driveline axis, at which the kinetic friction forces are applied at the frictional surfaces. It is related to the geometry of the conical friction surface geometry by:

`${r}_{\text{eff}}=\frac{1}{3\mathrm{sin}\alpha }\frac{{d}_{o}{}^{3}-{d}_{i}{}^{3}}{{d}_{o}{}^{2}-{d}_{i}{}^{2}}$`

do and di are the contact surface maximum and minimum diameters, respectively.

#### Static Friction

The static friction limit is related to the kinetic friction, setting ω to zero and replacing the kinetic with the static friction coefficient:

τS = kS·FN·reff ≥ 0 .

kS > kK, so that the torque τ needed across the clutch to unlock it by overcoming static friction is larger than the kinetic friction at the instant of unlocking, when ω = 0.

The static friction limit defines symmetric static friction torque limits as:

τSτS+ = –τS .

The range [τS, τS+] is used by the Fundamental Friction Clutch.

#### Engagement and Locking Conditions

The clutch engages (transmits torque) when the conical friction surfaces are subject to a positive normal force and generate kinetic friction: FN > 0 and τK> 0.

The clutch locks if and only if it is engaged, and the slip is less than the velocity tolerance: |ω| < ωTol.

#### Power Dissipated by the Clutch

The power dissipated by the clutch is |ω·τK|. The clutch dissipates power only if it is both slipping (ω ≠ 0) and applying kinetic friction (τK > 0).

## Modeling Thermal Effects

You can model the effects of heat flow and temperature change through an optional thermal conserving port. By default, the thermal port is hidden. To expose the thermal port, right-click the block in your model and, from the context menu, select Simscape > Block choices. Choose a variant that includes a thermal port. Specify the associated thermal parameters for the component.

## Ports

`B`

Rotational conserving ports associated with the driving (base) shaft. The clutch motion is measured as the slip ω = ωFωB, the angular velocity of follower relative to base.

`F`

Rotational conserving ports associated with the driven (follower) shaft

`N`

Physical signal terminal through which you import the normal force. This signal is positive or zero. A signal N less than zero is interpreted as zero.

`H`

Thermal conserving port. The thermal port is optional and is hidden by default. To expose the port, select a variant that includes a thermal port.

## Parameters

### Geometry

Contact surface maximum diameter

Outer conical diameter do. The default value is `150` `mm`.

Contact surface minimum diameter

Inner conical diameter di. The default value is `100` `mm`.

Cone half angle

Half opening angle α of the cone geometry. The default value is `12` `deg`.

### Friction

Friction model

Select a parameterization method to model the kinetic friction coefficient. The options and default values for this parameter depend on the variant that you select for the block. The options are:

• `Fixed kinetic friction coefficient` — Provide a fixed value for the kinetic friction coefficient. This option:

• Is only visible if you use the default variant of the block

• Is the default method for parameterizing the default variant of the block

• Affects the visibility of other parameters

• `Table lookup kinetic friction coefficient` — Define the kinetic friction coefficient by one-dimensional table lookup based on the relative angular velocity between disks. This option:

• Is only visible if you use the default variant of the block

• Affects the visibility of other parameters

• ```Temperature-dependent kinetic friction coefficient``` — Define the kinetic friction coefficient by table lookup based on the temperature. This option:

• Is only visible if you use a thermal variant of the block

• Is the default method for parameterizing the thermal variant of the block

• Affects the visibility of other parameters

• ```Temperature and speed-dependent kinetic friction coefficient``` — Define the kinetic friction coefficient by table lookup based on the temperature and the relative angular velocity between disks. This option:

• Is only visible if you use the default variant of the block

• Affects the visibility of other parameters

Velocity tolerance

Relative velocity below which the two surfaces can lock. The surfaces lock if the torque across the B and F rotational ports is less than the product of the effective radius, the static friction coefficient, and the applied normal force. The default value is `0.001` `rad/s`.

Threshold force

The normal force applied to the physical signal port N is applied to the contact only if the amount of force exceeds the value of the Threshold force parameter. Forces below the Threshold force are not applied, and there is consequently no transmitted frictional torque. The default value is `1` `N`.

### Initial Conditions

Initial state

Clutch state at the start of simulation. The clutch can be in one of two states, locked and unlocked. A locked clutch constrains the base and follower shafts to spin at the same velocity, i.e., as a single unit. An unlocked clutch allows the two shafts to spin at different velocities, resulting in slip between the clutch plates. The default setting is `Unlocked`.

### Thermal Port

These thermal parameters are visible only when you select a block variant that includes a thermal port.

Thermal mass

Thermal energy required to change the component temperature by a single degree. The greater the thermal mass, the more resistant the component is to temperature change. The default value is 25 `kJ/K`.

Initial temperature

Component temperature at the start of simulation. The initial temperature influences the starting meshing or friction losses by altering the component efficiency according to an efficiency vector that you specify. The default value is `300` `K`.

## Related Examples

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